Open Quantum Dynamics of Mesoscopic Bose-Einstein ... - Physics

2. Properties of an atomic Bose condensate in a double-well potentialFigure 2.19: Conditional (continuous line) and unconditional (dashed line) evolution of a 100-atom condensate in a noisy double-well potential, in the absence of collisions. The unconditionalevolution is calculated from 100 trajectories. In (a), γ/Ω =10and in (b), γ/Ω = 100. The timeaxis has been scaled by t 0 =1/Ω.0.5(a)0.5(b)00conditionalunconditionalno noise−0.588 90 92 94 96 98 100t/t 0conditionalunconditional−0.50 20 40t/t 060 80 100(2.86)) and is due to the phase kicks in individual trajectories. In Fig. 2.19(b), the increasednoise (γ = 100Ω) partially suppresses at times the conditional oscillations, leadingto a faster decay of the unconditional dynamics.In a noise-free potential, the presence of atoms collisions induces a collapse in theoscillations, followed at sometime later by revivals. This happens on a faster time scalefor smaller numbers of atoms, as shown in Fig. 2.11. The collapses are due to the dephasingeffect of the nonlinearity, while the revivals come from the granularity of small quantumsystems, when all spectral components temporarily come back into phase. When a systemis coupled to the environment, the spectral components will decohere, thereby preventingrevivals.We see just this thing happening to the double condensates in a noisy potential. Figure2.20 shows that even when γ = 10Ω, the resultant decoherence accelerates the collapseand suppresses the revival that was seen in Fig. 2.11. For a weak noise source, as in Figs.2.20(a&b) where γ/Ω = 10, the suppression of revivals is only partial, but for a largernoise source, as in Figs. 2.20(c&d) where γ/Ω = 100, there is no hint of revivals.Even though the mean evolution oscillates very little, the individual trajectories mayat times tunnel vigorously. The longer-time simulations (Fig. 2.21) clearly illustrate this,where for γ/Ω = 100 (in Fig. 2.21(b)), the conditional evolution suddenly revives near the56